“2x-5y=a bx+10y=-8 In the system of equations above a and b are constants. If the system has infinitely many solutions what is the value of a?”

"For a system of equations like 2x-5y=a and bx+10y=-8 to have infinitely many solutions the equations must be dependent meaning one is a multiple of the other. Comparing coefficients the ratio 2/b = -5/10 = a/-8 must hold. Solving 2/b = -1/2 gives b = -4 and -5/10 = a/-8 gives a = 4. Thus a equals 4. This concept is key in linear algebra applied in optimization economics and engineering for solving systems and modeling relationships."